Finite Group Databasebeta

← C3×C5×#14559075 #49137365

Subgroups — C3×C5×#14559075 #49137365

Order 36300.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#11925893C211yesmaximal, characteristic
2C5×#14559075C311yesmaximal, characteristic, direct product factor, Hall
3C3×C5×#10597245C411yescharacteristic, complemented, Hall
4C3×C5×#92150—51nomaximal
5C3×#14559075C511yesmaximal, characteristic, direct product factor
6C5×#11925893C2×C311yescharacteristic
7C3×C5×C11⋊D11D511yescharacteristic
8C3×#11925893—22no—
9C3×#11925893C2×C511yescharacteristic
10C5×#10597245C3×C411yescharacteristic, complemented, Hall
11C5×#92150—51no—
12#14559075C3×C511yescharacteristic, direct product factor
13C3×C5×C112Dic511yescharacteristic, complemented
14C3×#10597245—22no—
15C3×#10597245C4×C511yescharacteristic, complemented
16C3×C5×AGL(1,𝔽11)—221no—
17C3×#92150—51noHall
18C5×C11⋊D11C3×D511yescharacteristic
19#11925893—22no—
20#11925893C2×C3×C511yescharacteristic
21C3×C5×C11⋊C5—441no—
22C3×C11⋊D11C5×D511yescharacteristic
23C5×C112C3×Dic511yescharacteristic, complemented
24#10597245—22no—
25#10597245C3×C4×C511yescharacteristic, complemented
26C5×AGL(1,𝔽11)—221no—
27#92150—51noHall
28C3×C112C5×Dic511yescharacteristic, complemented, Hall
29C3×C5×D11—221no—
30C3×C5×D11—1101no—
31C3×AGL(1,𝔽11)—221no—
32C3×AGL(1,𝔽11)—224no—
33C3×C5×Dic5—1211nomaximal, Hall
34C5×C11⋊C5—221no—
35C11⋊D11C3×C5×D511yescharacteristic
36C3×C5×C11—21no—
37C3×C5×C11—101no—
38C3×C11⋊C5—444no—
39C3×C11⋊C5—441no—
40C2×C3×C52—1211no—
41C112C3×C5×Dic511yescharacteristic, complemented, Sylow
42C5×D11—221no—
43C5×D11—1101no—
44AGL(1,𝔽11)—221no—
45AGL(1,𝔽11)—224no—
46C5×Dic5—1211noHall
47C3×C52—4841noHall
48C3×D11—221no—
49C3×D11—1101no—
50C3×C4×C5—6051no—
51C3×Dic5—1211no—
52C5×C11—21no—
53C5×C11—101no—
54C11⋊C5—444no—
55C11⋊C5—441no—
56C2×C52—1211no—
57C3×C11—21no—
58C3×C11—101no—
59C2×C3×C5—1211no—
60C2×C3×C5—1211no—
61C2×C3×C5—2422no—
62C52—4841noSylow
63D11—221no—
64D11—1101no—
65C4×C5—6051no—
66Dic5—1211no—
67C3×C5—4841no—
68C3×C5—4842no—
69C3×C5#1455907511yescharacteristic, direct product factor
70C3×C4—6051noHall
71C11—21no—
72C11—101no—
73C2×C5—1211no—
74C2×C5—1211no—
75C2×C5—2422no—
76C2×C3—1211no—
77C5—4841no—
78C5—4842no—
79C5C3×#1455907511yescharacteristic, direct product factor
80C4—6051noSylow
81C3C5×#1455907511yescharacteristic, direct product factor, Sylow
82C2—1211no—
subgroupG/H
center, hypercenterC3×C5#14559075
commutator, hypocenter#10597245C3×C4×C5
FrattiniC1G
Fitting, socleC3×C5×C112Dic5
prime radicalC3×C5×#11925893C2
cosocle#11925893C2×C3×C5
LCSG ▷ #10597245
UCSC1 ◁ C3×C5

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C5×#14559075C3direct (N × H)
3. C3×C5×#10597245C4semidirect
5. C3×#14559075C5direct (N × H)
10. C5×#10597245C3×C4semidirect
12. #14559075C3×C5direct (N × H)
13. C3×C5×C112Dic5semidirect
15. C3×#10597245C4×C5semidirect
23. C5×C112C3×Dic5semidirect
25. #10597245C3×C4×C5semidirect
28. C3×C112C5×Dic5semidirect
41. C112C3×C5×Dic5semidirect
69. C3×C5#14559075direct (N × H)
79. C5C3×#14559075direct (N × H)
81. C3C5×#14559075direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×C5×#119258932
C5×#145590753
C3×C5×#921505
C3×#145590755
C3×C5×Dic5121